相关论文: Quantum Block and Convolutional Codes from Self-or…
In their comment, de Almedia and Palazzo \cite{comment} discovered an error in my earlier paper concerning the construction of quantum convolutional codes (quant-ph/9712029). This error can be repaired by modifying the method of code…
In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…
In this paper we obtain the [60,30,12], [64,32,12], [68,34,12], [72,36,12] self-dual codes as tailbitting convolutional codes with the smallest constraint length K=9. In this construction one information bit is modulo two added to the one…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
The existence of self-correcting quantum memories in three dimensions is a long-standing open question at the interface between quantum computing and many-body physics. We take the perspective that large contributions to the entropy arising…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…
Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…
Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of…
This article presents new constructions of quantum error correcting Calderbank-Shor-Steane (CSS for short) codes. These codes are mainly obtained by Sloane's classical combinations of linear codes applied here to the case of self-orthogonal…
We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…